The generator matrix

 1  0  0  1  1  1  1  1  1  1  1
 0  1  0  1  0  0  0  0  0  0  0
 0  0  1  1  0  0  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0
 0  0  0  0  0  0  0  0  0  0  X

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+23x^2+163x^4+597x^6+1338x^8+1536x^9+1974x^10+5120x^11+1974x^12+1536x^13+1338x^14+597x^16+163x^18+23x^20+1x^22

The gray image is a linear code over GF(2) with n=22, k=14 and d=2.
This code was found by Heurico 1.16 in 0.228 seconds.